course is different from what we have in class, so do not rely on these materials too much!) For the 1111 course, the final mark is 100*final exam mark or 80*final exam mark 20*home assignments result, whichever is higher. Cramer's rule for systems with the same number of equations and unknowns. For the second part of the course (abstract vector spaces, linear operators, quadratic forms etc.) the exposition will be mostly close to the one from Gelfand's "Lectures on Linear Algebra" (there should be several copies in the College Library, also some 20 copies belonging. Examples on computations with Jordan normal forms. For the first part of the course (Linear Algebra in 2d and 3d, systems of linear equations, operations with matrices have a glance at Anton/Rorres's "Elementary Linear Algebra (applications version. Any views expressed here do not necessarily represent the official views of Trinity College Dublin. Examples on Jordan forms for nilpotent operators. Linear independence and completeness. Same is true for the Halmos's book: click here.
Too Much Calculus Gilbert Strang (2001) pdf Hacker News
Linear algebra, TCD 2010/11
Orthonormal bases; Gram-Schmidt orthogonalisation. Dot and cross products. Principal and free variables. Examples (operators with A2A). An application: two commuting linear operators have a common eigenvector. Computing the inverse matrix using determinants. Minimal polynomial of a linear operator.
Similar matrices define the same linear operator in different bases. Jordan normal form (Jordan Decomposition Theorem). PDF, linear operators, matrices, change of coordinates: a brief howto.